At an event held at the stadium, 80% of the audience were adults. The female audience was made up of 40% of the adults and 70% of the children. There were 12 less boys than girls.
- How many people went to the stadium in total?
- Some women left before the event ended, after which 25% of the remaining people at the stadium were women. How many women left the stadium before it ended?
|
Adults |
Children |
Total |
|
4 u |
1 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
1.6 u |
2.4 u |
0.7 u |
0.3 u |
|
Change |
- ? |
|
- ? |
After |
|
3.4 u |
|
Comparison in the end |
1 p |
3 p |
4 p |
(a)
80% =
80100 =
45Number of women
= 40% x 4 u
=
40100 x 4 u
= 1.6 u
Number of men
= 4 u - 1.6 u
= 2.4 u
Number of girls
= 70% x 1 u
=
70100 x 1 u
= 0.7 u
Number of boys
= 1 u - 0.7 u
= 0.3 u
Number of more girls than boys
= 0.7 u - 0.3 u
= 0.4 u
0.4 u = 12
1 u = 12 ÷ 0.4 = 30
Number of people
= 5 u
= 5 x 30
= 150
(b)
25% =
25100 =
14The total number of men and children in the end is repeated.
3.4 u = 3 p
Number of men and children
= 2.4 u + 1 u
= 3.4 u
= 3.4 x 30
= 102
3 p = 3.4 u
3 p = 102
1 p = 102 ÷ 3 = 34
Number of women in the end
= 1 p
= 34
Number of women at first
= 1.6 u
= 1.6 x 30
= 48
Number of women who left before the event ended
= 48 - 34
= 14
Answers: (a) 150; (b) 14